Self-organization and a.s. convergence of the one-dimensional Kohonen algorithm with non-uniformly distributed stimuli

Catherine Bouton and Gilles Pagès

Stochastic Processes and their Applications, 1993, vol. 47, issue 2, 249-274

Abstract: This paper shows that the 2-neighbour Kohonen algorithm is self-organizing under pretty general assumptions on the stimuli distribution [mu] (supp([mu]c) contains a non-empty open set) and is a.s. convergent--in a weakened sense--as soon as [mu] admits a log-concave density. The 0-neighbour algorithm is shown to have similar converging properties. Some numerical simulations illustrate the theoretical results and a counter-example provided by a specific class of density functions.

Keywords: Neural; networks; Stochastic; algorithms; Markov; chains (search for similar items in EconPapers)
Date: 1993
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